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2020 Moderate deviations and extinction of an epidemic
Etienne Pardoux
Electron. J. Probab. 25: 1-27 (2020). DOI: 10.1214/20-EJP428

Abstract

Consider an epidemic model with a constant flux of susceptibles, in a situation where the corresponding deterministic epidemic model has a unique stable endemic equilibrium. For the associated stochastic model, whose law of large numbers limit is the deterministic model, the disease free equilibrium is an absorbing state, which is reached soon or later by the process. However, for a large population size, i.e. when the stochastic model is close to its deterministic limit, the time needed for the stochastic perturbations to stop the epidemic may be enormous. In this paper, we discuss how the Central Limit Theorem, Moderate and Large Deviations allow us to give estimates of the extinction time of the epidemic.

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Etienne Pardoux. "Moderate deviations and extinction of an epidemic." Electron. J. Probab. 25 1 - 27, 2020. https://doi.org/10.1214/20-EJP428

Information

Received: 21 May 2019; Accepted: 31 January 2020; Published: 2020
First available in Project Euclid: 18 February 2020

zbMATH: 1445.60022
MathSciNet: MR4073686
Digital Object Identifier: 10.1214/20-EJP428

Subjects:
Primary: 60F05 , 60F10 , 60J75 , 92D30

Keywords: central limit theorem , extension of an epidemic , large deviations , Moderate deviations

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